Simplify 4x + 3 − 2x + 5
- Group the variable terms: 4x − 2x = 2x.
- Group the constants: 3 + 5 = 8.
- Write 2x + 8. Do not combine 2x and 8 into 10x.
Algebra tiles & equivalent expressions
Make the parts of an expression visible, including what cancels to zero.
Lesson 02 · Start where you need
Your learning goal
Represent signed terms, combine like terms, and explain why equivalent expressions have the same value.
Give each tile a meaning
An x-tile represents the value x and a unit tile represents 1. A negative x-tile represents −x; a negative unit tile represents −1. The display uses a long tile to distinguish x from 1. It is a symbolic model: the drawn length does not require x to be positive or to equal a particular number.
Words worth knowing
- Equivalent
- Having the same value for every permitted input.
- Zero pair
- Opposite terms whose sum is zero.
- Like terms
- Terms with the same variable part.
1
Make the idea visible.
Predict a change, adjust one value, then explain what stayed the same.
Tile shapes distinguish symbols; their lengths do not set x’s value. Blue is positive; red is negative. Signs and labels also identify each term.
Combine like terms
Three x-tiles and two x-tiles can be grouped as five x-tiles: 3x + 2x = 5x. Three x-tiles and two unit tiles represent 3x + 2, not 5x. Like terms share the same variable part. Keep x-terms separate from constants until a value of x is supplied.
Zero pairs preserve value
A positive unit and a negative unit sum to zero. Likewise, x + (−x) = 0 for every x. Removing a zero pair changes the collection’s appearance but not its total value. For 3x + 4 − x − 6, combine the x-terms to get 2x, and combine the constants to get −2: the equivalent expression is 2x − 2.
Test without mistaking a test for proof
Substituting x = 3 into 3x + 4 − x − 6 gives 4. Substituting into 2x − 2 also gives 4. This is a useful check. The reason they agree for every x is the valid grouping and cancellation of like terms, rather than the single numerical match.
Worked examples
Follow the reasoning.
Evaluate 2x − 2 when x = −3
- Substitute with brackets: 2(−3) − 2.
- Multiply to get −6, then subtract 2.
- The value is −8. Negative x-tiles need not have a negative drawn length.
Try it with support
Show your thinking.
Simplify 5x − 3x + 2 − 7.
Give me a hint
Group the x-terms and constants separately.
Compare a worked response
2x − 5
5x − 3x = 2x, while 2 − 7 = −5.
Does x + 1 simplify to 2x? Explain.
Give me a hint
Test x = 2, then describe the unlike terms.
Compare a worked response
No.
x and 1 are unlike terms. At x = 2, x + 1 = 3 while 2x = 4.
Independent practice
Check your understanding.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
Choose a response, then use the explanation to check your reasoning. This is practice, not a school mark.
Go further
Keep the connections close.
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